Horizontal & Vertical Translations

Front

What is a horizontal translation?

Back

A horizontal translation is a shift of a graph left or right on the coordinate plane. It occurs when the input of the function is altered by adding or subtracting a constant.

Front

What does the equation p(x) = f(x + 3) represent?

Back

The equation p(x) = f(x + 3) represents a horizontal translation of the function f(x) to the left by 3 units.

Front

What is a vertical translation?

Back

A vertical translation is a shift of a graph up or down on the coordinate plane. It occurs when a constant is added to or subtracted from the output of the function.

Front

What does the equation h(x) = f(x) + 2 represent?

Back

The equation h(x) = f(x) + 2 represents a vertical translation of the function f(x) upwards by 2 units.

Front

How does the equation g(x) = x^2 - 3 transform the graph of f(x) = x^2?

Back

The equation g(x) = x^2 - 3 translates the graph of f(x) = x^2 downwards by 3 units.

Front

What is the effect of adding a constant to a function?

Back

Adding a constant to a function results in a vertical translation of the graph. If the constant is positive, the graph shifts up; if negative, it shifts down.

Front

What is the effect of subtracting a constant from the input of a function?

Back

Subtracting a constant from the input of a function results in a horizontal translation of the graph to the right.

Front

What does the equation y = x^2 + 5 represent?

Back

The equation y = x^2 + 5 represents a vertical translation of the graph of y = x^2 upwards by 5 units.

Front

What transformation does f(x) - 4 represent?

Back

The transformation f(x) - 4 represents a vertical translation of the graph downwards by 4 units.

Front

What is the general form of a quadratic function?

Back

The general form of a quadratic function is f(x) = ax^2 + bx + c, where a, b, and c are constants.